Effects of the Magnetic Model of Interior Permanent Magnet Machine on MTPA, Flux Weakening and MTPV Evaluation

Abstract

Interior permanent-magnet synchronous machines are widely spreading in automotive and vehicle traction applications, because of their high efficiency over a wide speed range. This capability can be achieved by appropriated control strategies: Maximum Torque per Ampere (MTPA), Flux Weakening (FW) and Maximum Torque per Volt (MTPV). However, these control trajectories are often based on an simplified magnetic model of the electrical machine. In order to improve the evaluation of machine output capabilities, nonlinear magnetic behavior must be modeled. This is not only related to the final application with a given drive and control structure, but also during the design process of the electric machine. In the design process, the output torque Vs. speed characteristic must be calculated following MTPA, MTPV and FW in the most accurate way to avoid significant error. This paper proposes a set of algorithms to compute MTPA, FW and MTPV curves for interior permanent-magnet synchronous machines taking into account the machines’ nonlinearities caused by iron saturation and compares differed approaches to highlight the torque–speed capabilities for the same machine following different methods. The algorithms are based on the maps of the equivalent inductances of a reference interior permanent-magnet synchronous machine and inductances maps were obtained via 2-D Finite Element Analysis over the machine’s operating points in id−iq reference plane. The effects of different 2-D finite element methods are also computed by both standard nonlinear magnetostatic simulations and Frozen Permeability simulations. Results show that the nonlinear model computed via frozen permeability is more accurate than the conventional linear and nonlinear models computed via standard magnetostatic simulations; for this reason, during the electrical machine design, it is important to check the expected performance employing a complete inductance map and frozen permeability.

Improved Current and MTPA Control Characteristics Using FEM-Based Inductance Maps for Vector-Controlled IPM Motor

“…Based on this inductance map, the modified IPM voltage, torque, and MTPA trajectory Equations become (8), (9), and (10), respectively. An alternative method of MTPA control utilizing a FEM-based map was also reported in [36]. The true MTPA trajectory line considers the variation in inductance values due to magnetic saturation and is the trajectory line that produces the maximum torque for a given current input [26].…”

“…Based on this inductance map, the modified IPM voltage, torque, and MTPA trajectory Equations become (8), (9), and (10), respectively. An alternative method of MTPA control utilizing a FEM-based map was also reported in [36].…”

Nonlinear Magnetic Model of IPMSM Based on the Frozen Permeability Technique Utilized in Improved MTPA Control

“…Even permanent magnet flux linkage suffers variation due to pronounced magnetic saturation [5,6]. Therefore, parameter variation adversely affects the performance of traditional control strategies based on classical magnetic models [7][8][9]. Due to the magnetic nonlinearity of IPMSM and the emergence of its accompanying issues, the necessity for its more accurate and physically inspired modeling becomes significant [10][11][12][13][14].…”

“…Certainly, approaches using FEA for flux map calculation are also widespread in the literature [8,[15][16][17]. In Ref.…”

“…The frozen permeability technique is also used in Ref. [8], where it was solely applied to determine the inductance, which was subsequently employed in a straightforward manner as constant values in the control algorithms. Unquestionably, improved magnetic models are highly useful for implementing advanced control techniques [18][19][20].…”